Adding and Place Value of Large Numbers

• newEditor
• Math
• Regrouping
• 2nd Grade

Addition and Place Value of Large Numbers

Central focus: when ones make 10, we regroup to the tens place; the same idea works again from tens to hundreds in 3-digit addition.

Our learning goal

I can add 2-digit and 3-digit numbers by regrouping when a place value makes 10 or more.

I can identify Place Value up to 1,000 and expand my numbers

What words come to mind when you hear regrouping?

Use this to surface prior ideas such as carry over, tens, ones, bigger numbers, columns, or confusion points. Briefly connect student words to the lesson goal.

Place value helps us add

• Digits have a place: ones, tens, hundreds

• We add the same places together

• Ones with ones

• Tens with tens

• Hundreds with hundreds

Keep the language concrete. Point to columns if students are used to vertical addition.

What does regrouping mean?

Regrouping happens when a place value adds to 10 or more.

Then we make a new group in the next place.

10 ones = 1 ten

10 tens = 1 hundred

Use 'make a new group' as the main phrase. Avoid introducing too many synonyms at once.

Add without regrouping

Example: 24 + 35

• Ones: 4 + 5 = 9

• Tens: 2 tens + 3 tens = 5 tens

• Sum: 59

Show this first so students see the normal place-value pattern before the extra step of regrouping.

Add with regrouping in ones

Example: 27 + 18

• Ones: 7 + 8 = 15

• 15 ones = 1 ten and 5 ones

• Tens: 2 tens + 1 ten + 1 new ten = 4 tens

• Sum: 45

Emphasise that the extra ten comes from the ones column, not from nowhere.

What does Expanded Form mean?

Expanded form of a number is stretching each number out by its place value such as hundreds, tens, and ones then adding them all together.

816= 800+10+6

462

400

60

2

Think in groups of ten

• 13 ones is too many for the ones place

• Trade 10 ones for 1 ten

• Keep the extra ones in the ones place

10

1

1

1

Use drawings, counters, or base-ten blocks if possible to make the trade visible.

When do we regroup in addition?

A

At 10 or more

B

At 5 or more

C

Only at 100

D

Only in ones

Checks the key rule from slides 2-6: regroup when a place value totals 10 or more.

Complete the regrouping idea

When we add, we put ones with ones and tens with tens. If the ones make 10 or more, we trade 10 ones for 1 ten.

ones

tens

10 ones

1 ten

hundreds

9 ones

2 tens

1 one

Echoes the language from the place-value and regrouping slides. Students should recognise the trade of 10 ones for 1 ten.

Line up the columns

When numbers are written up and down:

• ones under ones

• tens under tens

• hundreds under hundreds

This helps each place value stay in the right column.

A common error is misaligned digits, especially when one number has fewer digits.

2-digit addition to 100 and above

Some 2-digit sums stay below 100.

Some go to 100 or more.

Examples:

• 46 + 23 = 69

• 58 + 27 = 85

• 67 + 38 = 105

This slide bridges the teacher goal of strengthening addition up to 100 and above.

Which sum is 100 or more?

A

46 + 23

B

58 + 27

C

67 + 38

D

24 + 35

Uses examples already shown on slide 8. Distractors are real sums from nearby slides.

What helps you most with 2-digit addition?

1

Line up columns

2

Add ones first

3

Make groups of ten

4

Check the sum

3-digit numbers use the same idea

• Add ones first

• Then add tens

• Then add hundreds

• Regroup whenever a place makes 10 or more

Stress continuity: 3-digit addition is not a new rule, only one more place value.

Regroup tens into hundreds

Example: 156 + 167

• Ones: 6 + 7 = 13 → 1 ten and 3 ones

• Tens: 5 tens + 6 tens + 1 ten = 12 tens

• 12 tens = 1 hundred and 2 tens

• Hundreds: 1 hundred + 1 hundred + 1 hundred = 3 hundreds

• Sum: 323

This is the key generalisation slide: regrouping can happen more than once in one problem.

Another 3-digit example

Example: 243 + 125

• Ones: 3 + 5 = 8

• Tens: 4 tens + 2 tens = 6 tens

• Hundreds: 2 hundreds + 1 hundred = 3 hundreds

• Sum: 368

Include one example without regrouping so students can compare and decide when regrouping is needed.

Another example of Expanded Form

Example: 1,864

• 1 is in the thousands place. So it is worth 1,000

• 8 is in the hundreds place. So it is worth 800

• 6 is in the tens place. So it is worth 60

• 4 is in the ones place. So it is worth 4

1,000+800+60+4

Watch for common mistakes

• Forgetting to add the new ten

• Writing digits in the wrong column

• Adding tens like ones

• Stopping after adding the ones

Good moment to model checking each column from right to left.

How to check your sum

• Start with the ones column

• Look for any place that is 10 or more

• Make the new group

• Read the final number carefully

Keep the checking routine simple and repeatable.

In 156 + 167, what does 12 tens become?

A

12 ones

B

2 hundreds

C

1 hundred and 2 tens

D

1 ten and 2 ones

Targets the key generalisation on slide 10: tens can regroup into hundreds.

Complete the 3-digit method

In 3-digit addition, start with the ones column. Then add the tens column. If a place makes 10 or more, make a new group in the next place.

ones

tens

group

next place

hundreds

same place

digit

answer

Summarises slides 9-13 using the lesson's own wording: ones, tens, regroup, next place.

What is one thing you learned today?

Reflection only. Invite short answers about regrouping, place value, or checking sums.

What helped you understand best?

Reflection only. Students may mention blocks, columns, examples, or making groups of ten.

What part still feels tricky?

Reflection only. Students may mention carrying to tens or hundreds, lining up columns, or remembering the new ten.

Glossary

add - to put numbers together to find the total

sum - the answer in an addition problem

place value - the value of a digit because of its place

ones - the place for single units

tens - the place for groups of ten

hundreds - the place for groups of one hundred

regrouping - making a new group when a place value adds to 10 or more